LMFDB - Embedded newform 64.22.e.a.17.39

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [64,22,Mod(17,64)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("64.17"); S:= CuspForms(chi, 22); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(64, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3])) N = Newforms(chi, 22, names="a")

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 22 $
Character orbit:	$[\chi]$	$=$	64.e (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$178.865500344$
Analytic rank:	$0$
Dimension:	$82$
Relative dimension:	$41$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.39
Character	$\chi$	$=$	64.17
Dual form			64.22.e.a.49.39

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(127691. + 127691. i) q^{3} +(6.46851e6 - 6.46851e6i) q^{5} +1.09329e9i q^{7} +2.21494e10i q^{9} +(-9.04627e10 + 9.04627e10i) q^{11} +(6.65615e10 + 6.65615e10i) q^{13} +1.65194e12 q^{15} -1.23211e13 q^{17} +(2.96854e13 + 2.96854e13i) q^{19} +(-1.39603e14 + 1.39603e14i) q^{21} +1.97243e14i q^{23} +3.93154e14i q^{25} +(-1.49258e15 + 1.49258e15i) q^{27} +(-9.11213e14 - 9.11213e14i) q^{29} +4.52120e15 q^{31} -2.31025e16 q^{33} +(7.07199e15 + 7.07199e15i) q^{35} +(2.37522e16 - 2.37522e16i) q^{37} +1.69985e16i q^{39} -4.95700e16i q^{41} +(5.80467e16 - 5.80467e16i) q^{43} +(1.43274e17 + 1.43274e17i) q^{45} -1.35072e17 q^{47} -6.36747e17 q^{49} +(-1.57329e18 - 1.57329e18i) q^{51} +(1.22723e18 - 1.22723e18i) q^{53} +1.17032e18i q^{55} +7.58110e18i q^{57} +(2.88659e18 - 2.88659e18i) q^{59} +(-2.51678e18 - 2.51678e18i) q^{61} -2.42158e19 q^{63} +8.61108e17 q^{65} +(-1.76441e18 - 1.76441e18i) q^{67} +(-2.51861e19 + 2.51861e19i) q^{69} +6.89277e18i q^{71} +2.30134e19i q^{73} +(-5.02020e19 + 5.02020e19i) q^{75} +(-9.89024e19 - 9.89024e19i) q^{77} -5.60462e18 q^{79} -1.49486e20 q^{81} +(5.63613e18 + 5.63613e18i) q^{83} +(-7.96993e19 + 7.96993e19i) q^{85} -2.32706e20i q^{87} -1.52218e20i q^{89} +(-7.27713e19 + 7.27713e19i) q^{91} +(5.77314e20 + 5.77314e20i) q^{93} +3.84041e20 q^{95} -2.96525e20 q^{97} +(-2.00369e21 - 2.00369e21i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 82 q + 2 q^{3} - 2 q^{5} - 67333320738 q^{11} - 2 q^{13} - 4613203124996 q^{15} - 4 q^{17} + 46007763621434 q^{19} + 20920706404 q^{21} - 11\!\cdots\!20 q^{27} - 24\!\cdots\!02 q^{29} + 98\!\cdots\!16 q^{31}+ \cdots - 27\!\cdots\!38 q^{99}+O(q^{100}) $ 82 * q + 2 * q^3 - 2 * q^5 - 67333320738 * q^11 - 2 * q^13 - 4613203124996 * q^15 - 4 * q^17 + 46007763621434 * q^19 + 20920706404 * q^21 - 1147760716556920 * q^27 - 2433173450216602 * q^29 + 9835539443769616 * q^31 - 4 * q^33 + 19253478556034884 * q^35 - 7245708527119386 * q^37 - 215332019803969386 * q^43 + 953653395699842 * q^45 - 1051982644716600976 * q^47 - 5585458640832840074 * q^49 - 3238772068175213124 * q^51 + 1889987679210147606 * q^53 - 3631979197965016922 * q^59 + 10385362452353654062 * q^61 + 17464422381302680956 * q^63 - 9364161130572538716 * q^65 + 17102217044572669130 * q^67 - 3951842785111207532 * q^69 - 145960939174166395366 * q^75 - 82041801652678580764 * q^77 - 204448210818924484480 * q^79 - 802405920297757300870 * q^81 - 317463236552669319678 * q^83 + 323656241286464843748 * q^85 - 144326756239046079748 * q^91 - 669717759565183008560 * q^93 + 1411330138695550130700 * q^95 - 4 * q^97 - 2710306841526615010238 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/64\mathbb{Z}\right)^\times$.

$n$	$5$	$63$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	127691.	+	127691.i	1.24849	+	1.24849i	0.956386	+	0.292105i	$0.0943556\pi$
$3$	127691.	+	127691.i	1.24849	+	1.24849i	0.292105	+	0.956386i	$0.405644\pi$
$4$		0			0
$5$	6.46851e6	−	6.46851e6i	0.296223	−	0.296223i	−0.543309	−	0.839533i	$-0.682829\pi$
$5$	6.46851e6	−	6.46851e6i	0.296223	−	0.296223i	0.839533	+	0.543309i	$0.182829\pi$
$6$		0			0
$7$			1.09329e9i			1.46288i	0.681907	+	0.731438i	$0.261151\pi$
$7$			1.09329e9i			1.46288i	−0.681907	+	0.731438i	$0.738849\pi$
$8$		0			0
$9$			2.21494e10i			2.11746i
$10$		0			0
$11$	−9.04627e10	+	9.04627e10i	−1.05159	+	1.05159i	−0.0529954	+	0.998595i	$0.516877\pi$
$11$	−9.04627e10	+	9.04627e10i	−1.05159	+	1.05159i	−0.998595	+	0.0529954i	$0.983123\pi$
$12$		0			0
$13$	6.65615e10	+	6.65615e10i	0.133911	+	0.133911i	0.770885	−	0.636974i	$-0.219814\pi$
$13$	6.65615e10	+	6.65615e10i	0.133911	+	0.133911i	−0.636974	+	0.770885i	$0.719814\pi$
$14$		0			0
$15$	1.65194e12			0.739665
$16$		0			0
$17$	−1.23211e13			−1.48230			−0.741151	−	0.671339i	$-0.765720\pi$
$17$	−1.23211e13			−1.48230			−0.741151	+	0.671339i	$0.765720\pi$
$18$		0			0
$19$	2.96854e13	+	2.96854e13i	1.11079	+	1.11079i	0.993044	+	0.117743i	$0.0375659\pi$
$19$	2.96854e13	+	2.96854e13i	1.11079	+	1.11079i	0.117743	+	0.993044i	$0.462434\pi$
$20$		0			0
$21$	−1.39603e14	+	1.39603e14i	−1.82639	+	1.82639i
$22$		0			0
$23$			1.97243e14i			0.992796i	0.868095	+	0.496398i	$0.165344\pi$
$23$			1.97243e14i			0.992796i	−0.868095	+	0.496398i	$0.834656\pi$
$24$		0			0
$25$			3.93154e14i			0.824503i
$26$		0			0
$27$	−1.49258e15	+	1.49258e15i	−1.39514	+	1.39514i
$28$		0			0
$29$	−9.11213e14	−	9.11213e14i	−0.402199	−	0.402199i	0.476808	−	0.879007i	$-0.341794\pi$
$29$	−9.11213e14	−	9.11213e14i	−0.402199	−	0.402199i	−0.879007	+	0.476808i	$0.841794\pi$
$30$		0			0
$31$	4.52120e15			0.990730			0.495365	−	0.868685i	$-0.335034\pi$
$31$	4.52120e15			0.990730			0.495365	+	0.868685i	$0.335034\pi$
$32$		0			0
$33$	−2.31025e16			−2.62580
$34$		0			0
$35$	7.07199e15	+	7.07199e15i	0.433338	+	0.433338i
$36$		0			0
$37$	2.37522e16	−	2.37522e16i	0.812056	−	0.812056i	−0.172886	−	0.984942i	$-0.555309\pi$
$37$	2.37522e16	−	2.37522e16i	0.812056	−	0.812056i	0.984942	+	0.172886i	$0.0553092\pi$
$38$		0			0
$39$			1.69985e16i			0.334375i
$40$		0			0
$41$		−	4.95700e16i		−	0.576751i	−0.957517	−	0.288375i	$-0.906885\pi$
$41$		−	4.95700e16i		−	0.576751i	0.957517	−	0.288375i	$-0.0931151\pi$
$42$		0			0
$43$	5.80467e16	−	5.80467e16i	0.409599	−	0.409599i	−0.472000	−	0.881599i	$-0.656468\pi$
$43$	5.80467e16	−	5.80467e16i	0.409599	−	0.409599i	0.881599	+	0.472000i	$0.156468\pi$
$44$		0			0
$45$	1.43274e17	+	1.43274e17i	0.627241	+	0.627241i
$46$		0			0
$47$	−1.35072e17			−0.374573			−0.187287	−	0.982305i	$-0.559969\pi$
$47$	−1.35072e17			−0.374573			−0.187287	+	0.982305i	$0.559969\pi$
$48$		0			0
$49$	−6.36747e17			−1.14001
$50$		0			0
$51$	−1.57329e18	−	1.57329e18i	−1.85064	−	1.85064i
$52$		0			0
$53$	1.22723e18	−	1.22723e18i	0.963891	−	0.963891i	−0.0354791	−	0.999370i	$-0.511296\pi$
$53$	1.22723e18	−	1.22723e18i	0.963891	−	0.963891i	0.999370	+	0.0354791i	$0.0112957\pi$
$54$		0			0
$55$			1.17032e18i			0.623011i
$56$		0			0
$57$			7.58110e18i			2.77362i
$58$		0			0
$59$	2.88659e18	−	2.88659e18i	0.735257	−	0.735257i	−0.236399	−	0.971656i	$-0.575967\pi$
$59$	2.88659e18	−	2.88659e18i	0.735257	−	0.735257i	0.971656	+	0.236399i	$0.0759673\pi$
$60$		0			0
$61$	−2.51678e18	−	2.51678e18i	−0.451733	−	0.451733i	0.444197	−	0.895929i	$-0.353489\pi$
$61$	−2.51678e18	−	2.51678e18i	−0.451733	−	0.451733i	−0.895929	+	0.444197i	$0.853489\pi$
$62$		0			0
$63$	−2.42158e19			−3.09758
$64$		0			0
$65$	8.61108e17			0.0793354
$66$		0			0
$67$	−1.76441e18	−	1.76441e18i	−0.118254	−	0.118254i	0.645504	−	0.763757i	$-0.276648\pi$
$67$	−1.76441e18	−	1.76441e18i	−0.118254	−	0.118254i	−0.763757	+	0.645504i	$0.776648\pi$
$68$		0			0
$69$	−2.51861e19	+	2.51861e19i	−1.23950	+	1.23950i
$70$		0			0
$71$			6.89277e18i			0.251293i	0.992075	+	0.125647i	$0.0401006\pi$
$71$			6.89277e18i			0.251293i	−0.992075	+	0.125647i	$0.959899\pi$
$72$		0			0
$73$			2.30134e19i			0.626746i	0.949630	+	0.313373i	$0.101459\pi$
$73$			2.30134e19i			0.626746i	−0.949630	+	0.313373i	$0.898541\pi$
$74$		0			0
$75$	−5.02020e19	+	5.02020e19i	−1.02939	+	1.02939i
$76$		0			0
$77$	−9.89024e19	−	9.89024e19i	−1.53835	−	1.53835i
$78$		0			0
$79$	−5.60462e18			−0.0665981			−0.0332991	−	0.999445i	$-0.510601\pi$
$79$	−5.60462e18			−0.0665981			−0.0332991	+	0.999445i	$0.510601\pi$
$80$		0			0
$81$	−1.49486e20			−1.36618
$82$		0			0
$83$	5.63613e18	+	5.63613e18i	0.0398713	+	0.0398713i	0.726761	−	0.686890i	$-0.241025\pi$
$83$	5.63613e18	+	5.63613e18i	0.0398713	+	0.0398713i	−0.686890	+	0.726761i	$0.741025\pi$
$84$		0			0
$85$	−7.96993e19	+	7.96993e19i	−0.439092	+	0.439092i
$86$		0			0
$87$		−	2.32706e20i		−	1.00428i
$88$		0			0
$89$		−	1.52218e20i		−	0.517454i	−0.965950	−	0.258727i	$-0.916697\pi$
$89$		−	1.52218e20i		−	0.517454i	0.965950	−	0.258727i	$-0.0833031\pi$
$90$		0			0
$91$	−7.27713e19	+	7.27713e19i	−0.195896	+	0.195896i
$92$		0			0
$93$	5.77314e20	+	5.77314e20i	1.23692	+	1.23692i
$94$		0			0
$95$	3.84041e20			0.658082
$96$		0			0
$97$	−2.96525e20			−0.408280			−0.204140	−	0.978942i	$-0.565440\pi$
$97$	−2.96525e20			−0.408280			−0.204140	+	0.978942i	$0.565440\pi$
$98$		0			0
$99$	−2.00369e21	−	2.00369e21i	−2.22670	−	2.22670i
$100$		0			0
$101$	−3.30198e20	+	3.30198e20i	−0.297441	+	0.297441i	−0.840011	−	0.542570i	$-0.817451\pi$
$101$	−3.30198e20	+	3.30198e20i	−0.297441	+	0.297441i	0.542570	+	0.840011i	$0.317451\pi$
$102$		0			0
$103$			1.54573e21i			1.13330i	0.823960	+	0.566648i	$0.191760\pi$
$103$			1.54573e21i			1.13330i	−0.823960	+	0.566648i	$0.808240\pi$
$104$		0			0
$105$			1.80605e21i			1.08204i
$106$		0			0
$107$	1.29617e21	−	1.29617e21i	0.636989	−	0.636989i	−0.312823	−	0.949812i	$-0.601275\pi$
$107$	1.29617e21	−	1.29617e21i	0.636989	−	0.636989i	0.949812	+	0.312823i	$0.101275\pi$
$108$		0			0
$109$	1.86079e21	+	1.86079e21i	0.752867	+	0.752867i	0.975013	−	0.222147i	$-0.0713064\pi$
$109$	1.86079e21	+	1.86079e21i	0.752867	+	0.752867i	−0.222147	+	0.975013i	$0.571306\pi$
$110$		0			0
$111$	6.06586e21			2.02769
$112$		0			0
$113$	6.20544e21			1.71968			0.859842	−	0.510560i	$-0.170562\pi$
$113$	6.20544e21			1.71968			0.859842	+	0.510560i	$0.170562\pi$
$114$		0			0
$115$	1.27587e21	+	1.27587e21i	0.294089	+	0.294089i
$116$		0			0
$117$	−1.47430e21	+	1.47430e21i	−0.283552	+	0.283552i
$118$		0			0
$119$		−	1.34706e22i		−	2.16842i
$120$		0			0
$121$		−	8.96676e21i		−	1.21168i
$122$		0			0
$123$	6.32962e21	−	6.32962e21i	0.720068	−	0.720068i
$124$		0			0
$125$	5.62755e21	+	5.62755e21i	0.540461	+	0.540461i
$126$		0			0
$127$	1.34643e20			0.0109457			0.00547286	−	0.999985i	$-0.498258\pi$
$127$	1.34643e20			0.0109457			0.00547286	+	0.999985i	$0.498258\pi$
$128$		0			0
$129$	1.48240e22			1.02276
$130$		0			0
$131$	−1.36500e22	−	1.36500e22i	−0.801279	−	0.801279i	0.182017	−	0.983295i	$-0.441738\pi$
$131$	−1.36500e22	−	1.36500e22i	−0.801279	−	0.801279i	−0.983295	+	0.182017i	$0.941738\pi$
$132$		0			0
$133$	−3.24549e22	+	3.24549e22i	−1.62494	+	1.62494i
$134$		0			0
$135$			1.93095e22i			0.826545i
$136$		0			0
$137$			9.56736e21i			0.350935i	0.984485	+	0.175467i	$0.0561436\pi$
$137$			9.56736e21i			0.350935i	−0.984485	+	0.175467i	$0.943856\pi$
$138$		0			0
$139$	−2.93604e22	+	2.93604e22i	−0.924925	+	0.924925i	−0.997372	−	0.0724475i	$-0.976919\pi$
$139$	−2.93604e22	+	2.93604e22i	−0.924925	+	0.924925i	0.0724475	+	0.997372i	$0.476919\pi$
$140$		0			0
$141$	−1.72474e22	−	1.72474e22i	−0.467651	−	0.467651i
$142$		0			0
$143$	−1.20427e22			−0.281640
$144$		0			0
$145$	−1.17884e22			−0.238281
$146$		0			0
$147$	−8.13066e22	−	8.13066e22i	−1.42329	−	1.42329i
$148$		0			0
$149$	−5.13045e22	+	5.13045e22i	−0.779292	+	0.779292i	−0.979710	−	0.200419i	$-0.935770\pi$
$149$	−5.13045e22	+	5.13045e22i	−0.779292	+	0.779292i	0.200419	+	0.979710i	$0.435770\pi$
$150$		0			0
$151$			1.19676e23i			1.58033i	0.612893	+	0.790166i	$0.290006\pi$
$151$			1.19676e23i			1.58033i	−0.612893	+	0.790166i	$0.709994\pi$
$152$		0			0
$153$		−	2.72905e23i		−	3.13871i
$154$		0			0
$155$	2.92454e22	−	2.92454e22i	0.293478	−	0.293478i
$156$		0			0
$157$	−5.54236e22	−	5.54236e22i	−0.486126	−	0.486126i	0.420956	−	0.907081i	$-0.361695\pi$
$157$	−5.54236e22	−	5.54236e22i	−0.486126	−	0.486126i	−0.907081	+	0.420956i	$0.861695\pi$
$158$		0			0
$159$	3.13410e23			2.40682
$160$		0			0
$161$	−2.15645e23			−1.45234
$162$		0			0
$163$	−1.91177e23	−	1.91177e23i	−1.13101	−	1.13101i	−0.990010	−	0.140995i	$-0.954970\pi$
$163$	−1.91177e23	−	1.91177e23i	−1.13101	−	1.13101i	−0.140995	−	0.990010i	$-0.545030\pi$
$164$		0			0
$165$	−1.49439e23	+	1.49439e23i	−0.777824	+	0.777824i
$166$		0			0
$167$			1.02442e23i			0.469848i	0.972014	+	0.234924i	$0.0754841\pi$
$167$			1.02442e23i			0.469848i	−0.972014	+	0.234924i	$0.924516\pi$
$168$		0			0
$169$		−	2.38204e23i		−	0.964135i
$170$		0			0
$171$	−6.57514e23	+	6.57514e23i	−2.35205	+	2.35205i
$172$		0			0
$173$	3.70272e23	+	3.70272e23i	1.17230	+	1.17230i	0.981661	+	0.190634i	$0.0610545\pi$
$173$	3.70272e23	+	3.70272e23i	1.17230	+	1.17230i	0.190634	+	0.981661i	$0.438945\pi$
$174$		0			0
$175$	−4.29833e23			−1.20615
$176$		0			0
$177$	7.37180e23			1.83592
$178$		0			0
$179$	−8.53306e22	−	8.53306e22i	−0.188863	−	0.188863i	0.606341	−	0.795205i	$-0.292637\pi$
$179$	−8.53306e22	−	8.53306e22i	−0.188863	−	0.188863i	−0.795205	+	0.606341i	$0.792637\pi$
$180$		0			0
$181$	−1.04338e23	+	1.04338e23i	−0.205503	+	0.205503i	−0.802353	−	0.596850i	$-0.796419\pi$
$181$	−1.04338e23	+	1.04338e23i	−0.205503	+	0.205503i	0.596850	+	0.802353i	$0.296419\pi$
$182$		0			0
$183$		−	6.42737e23i		−	1.12797i
$184$		0			0
$185$		−	3.07283e23i		−	0.481100i
$186$		0			0
$187$	1.11460e24	−	1.11460e24i	1.55877	−	1.55877i
$188$		0			0
$189$	−1.63183e24	−	1.63183e24i	−2.04092	−	2.04092i
$190$		0			0
$191$	1.11757e24			1.25148			0.625739	−	0.780033i	$-0.284798\pi$
$191$	1.11757e24			1.25148			0.625739	+	0.780033i	$0.284798\pi$
$192$		0			0
$193$	9.81338e22			0.0985070			0.0492535	−	0.998786i	$-0.484316\pi$
$193$	9.81338e22			0.0985070			0.0492535	+	0.998786i	$0.484316\pi$
$194$		0			0
$195$	1.09955e23	+	1.09955e23i	0.0990496	+	0.0990496i
$196$		0			0
$197$	1.71171e24	−	1.71171e24i	1.38527	−	1.38527i	0.550307	−	0.834962i	$-0.314511\pi$
$197$	1.71171e24	−	1.71171e24i	1.38527	−	1.38527i	0.834962	−	0.550307i	$-0.185489\pi$
$198$		0			0
$199$			9.27620e23i			0.675170i	0.941295	+	0.337585i	$0.109610\pi$
$199$			9.27620e23i			0.675170i	−0.941295	+	0.337585i	$0.890390\pi$
$200$		0			0
$201$		−	4.50597e23i		−	0.295277i
$202$		0			0
$203$	9.96224e23	−	9.96224e23i	0.588367	−	0.588367i
$204$		0			0
$205$	−3.20644e23	−	3.20644e23i	−0.170847	−	0.170847i
$206$		0			0
$207$	−4.36882e24			−2.10221
$208$		0			0
$209$	−5.37085e24			−2.33619
$210$		0			0
$211$	4.36535e22	+	4.36535e22i	0.0171812	+	0.0171812i	0.715645	−	0.698464i	$-0.246133\pi$
$211$	4.36535e22	+	4.36535e22i	0.0171812	+	0.0171812i	−0.698464	+	0.715645i	$0.746133\pi$
$212$		0			0
$213$	−8.80141e23	+	8.80141e23i	−0.313737	+	0.313737i
$214$		0			0
$215$		−	7.50951e23i		−	0.242665i
$216$		0			0
$217$			4.94300e24i			1.44932i
$218$		0			0
$219$	−2.93860e24	+	2.93860e24i	−0.782486	+	0.782486i
$220$		0			0
$221$	−8.20112e23	−	8.20112e23i	−0.198497	−	0.198497i
$222$		0			0
$223$	−8.06105e24			−1.77497			−0.887484	−	0.460839i	$-0.847548\pi$
$223$	−8.06105e24			−1.77497			−0.887484	+	0.460839i	$0.847548\pi$
$224$		0			0
$225$	−8.70811e24			−1.74585
$226$		0			0
$227$	−4.51946e24	−	4.51946e24i	−0.825686	−	0.825686i	0.161231	−	0.986917i	$-0.448454\pi$
$227$	−4.51946e24	−	4.51946e24i	−0.825686	−	0.825686i	−0.986917	+	0.161231i	$0.948454\pi$
$228$		0			0
$229$	−1.32722e24	+	1.32722e24i	−0.221142	+	0.221142i	−0.808979	−	0.587837i	$-0.799979\pi$
$229$	−1.32722e24	+	1.32722e24i	−0.221142	+	0.221142i	0.587837	+	0.808979i	$0.299979\pi$
$230$		0			0
$231$		−	2.52578e25i		−	3.84122i
$232$		0			0
$233$		−	1.07270e24i		−	0.149019i	−0.997220	−	0.0745095i	$-0.976261\pi$
$233$		−	1.07270e24i		−	0.149019i	0.997220	−	0.0745095i	$-0.0237391\pi$
$234$		0			0
$235$	−8.73713e23	+	8.73713e23i	−0.110957	+	0.110957i
$236$		0			0
$237$	−7.15657e23	−	7.15657e23i	−0.0831471	−	0.0831471i
$238$		0			0
$239$	−1.44562e25			−1.53771			−0.768856	−	0.639423i	$-0.779173\pi$
$239$	−1.44562e25			−1.53771			−0.768856	+	0.639423i	$0.779173\pi$
$240$		0			0
$241$	4.34920e24			0.423868			0.211934	−	0.977284i	$-0.432024\pi$
$241$	4.34920e24			0.423868			0.211934	+	0.977284i	$0.432024\pi$
$242$		0			0
$243$	−3.47501e24	−	3.47501e24i	−0.310520	−	0.310520i
$244$		0			0
$245$	−4.11881e24	+	4.11881e24i	−0.337697	+	0.337697i
$246$		0			0
$247$			3.95182e24i			0.297494i
$248$		0			0
$249$			1.43936e24i			0.0995580i
$250$		0			0
$251$	6.83809e24	−	6.83809e24i	0.434871	−	0.434871i	−0.455410	−	0.890282i	$-0.650507\pi$
$251$	6.83809e24	−	6.83809e24i	0.434871	−	0.434871i	0.890282	+	0.455410i	$0.150507\pi$
$252$		0			0
$253$	−1.78432e25	−	1.78432e25i	−1.04401	−	1.04401i
$254$		0			0
$255$	−2.03537e25			−1.09641
$256$		0			0
$257$	−1.42894e25			−0.709115			−0.354557	−	0.935034i	$-0.615368\pi$
$257$	−1.42894e25			−0.709115			−0.354557	+	0.935034i	$0.615368\pi$
$258$		0			0
$259$	2.59682e25	+	2.59682e25i	1.18794	+	1.18794i
$260$		0			0
$261$	2.01828e25	−	2.01828e25i	0.851640	−	0.851640i
$262$		0			0
$263$			4.82269e24i			0.187825i	0.995580	+	0.0939126i	$0.0299374\pi$
$263$			4.82269e24i			0.187825i	−0.995580	+	0.0939126i	$0.970063\pi$
$264$		0			0
$265$		−	1.58767e25i		−	0.571054i
$266$		0			0
$267$	1.94368e25	−	1.94368e25i	0.646037	−	0.646037i
$268$		0			0
$269$	−1.44174e25	−	1.44174e25i	−0.443085	−	0.443085i	0.449962	−	0.893048i	$-0.351437\pi$
$269$	−1.44174e25	−	1.44174e25i	−0.443085	−	0.443085i	−0.893048	+	0.449962i	$0.851437\pi$
$270$		0			0
$271$	5.03629e25			1.43197			0.715983	−	0.698117i	$-0.245979\pi$
$271$	5.03629e25			1.43197			0.715983	+	0.698117i	$0.245979\pi$
$272$		0			0
$273$	−1.85844e25			−0.489149
$274$		0			0
$275$	−3.55658e25	−	3.55658e25i	−0.867040	−	0.867040i
$276$		0			0
$277$	4.43100e25	−	4.43100e25i	1.00107	−	1.00107i	0.00107069	−	0.999999i	$-0.499659\pi$
$277$	4.43100e25	−	4.43100e25i	1.00107	−	1.00107i	0.999999	−	0.00107069i	$-0.000340810\pi$
$278$		0			0
$279$			1.00142e26i			2.09783i
$280$		0			0
$281$			8.99135e23i			0.0174747i	0.999962	+	0.00873733i	$0.00278121\pi$
$281$			8.99135e23i			0.0174747i	−0.999962	+	0.00873733i	$0.997219\pi$
$282$		0			0
$283$	−2.47394e25	+	2.47394e25i	−0.446306	+	0.446306i	−0.894124	−	0.447819i	$-0.852201\pi$
$283$	−2.47394e25	+	2.47394e25i	−0.446306	+	0.446306i	0.447819	+	0.894124i	$0.352201\pi$
$284$		0			0
$285$	4.90384e25	+	4.90384e25i	0.821610	+	0.821610i
$286$		0			0
$287$	5.41946e25			0.843716
$288$		0			0
$289$	8.27181e25			1.19722
$290$		0			0
$291$	−3.78635e25	−	3.78635e25i	−0.509734	−	0.509734i
$292$		0			0
$293$	−1.09210e26	+	1.09210e26i	−1.36821	+	1.36821i	−0.505227	+	0.862986i	$0.668591\pi$
$293$	−1.09210e26	+	1.09210e26i	−1.36821	+	1.36821i	−0.862986	+	0.505227i	$0.831409\pi$
$294$		0			0
$295$		−	3.73439e25i		−	0.435600i
$296$		0			0
$297$		−	2.70045e26i		−	2.93423i
$298$		0			0
$299$	−1.31288e25	+	1.31288e25i	−0.132947	+	0.132947i
$300$		0			0
$301$	6.34621e25	+	6.34621e25i	0.599193	+	0.599193i
$302$		0			0
$303$	−8.43264e25			−0.742704
$304$		0			0
$305$	−3.25596e25			−0.267628
$306$		0			0
$307$	8.69206e25	+	8.69206e25i	0.667068	+	0.667068i	0.957036	−	0.289969i	$-0.0936448\pi$
$307$	8.69206e25	+	8.69206e25i	0.667068	+	0.667068i	−0.289969	+	0.957036i	$0.593645\pi$
$308$		0			0
$309$	−1.97375e26	+	1.97375e26i	−1.41491	+	1.41491i
$310$		0			0
$311$		−	7.56721e25i		−	0.506934i	−0.967344	−	0.253467i	$-0.918429\pi$
$311$		−	7.56721e25i		−	0.506934i	0.967344	−	0.253467i	$-0.0815709\pi$
$312$		0			0
$313$			8.29325e25i			0.519409i	0.965688	+	0.259704i	$0.0836251\pi$
$313$			8.29325e25i			0.519409i	−0.965688	+	0.259704i	$0.916375\pi$
$314$		0			0
$315$	−1.56640e26	+	1.56640e26i	−0.917577	+	0.917577i
$316$		0			0
$317$	−1.02487e26	−	1.02487e26i	−0.561752	−	0.561752i	0.368053	−	0.929805i	$-0.380025\pi$
$317$	−1.02487e26	−	1.02487e26i	−0.561752	−	0.561752i	−0.929805	+	0.368053i	$0.880025\pi$
$318$		0			0
$319$	1.64862e26			0.845897
$320$		0			0
$321$	3.31017e26			1.59055
$322$		0			0
$323$	−3.65758e26	−	3.65758e26i	−1.64652	−	1.64652i
$324$		0			0
$325$	−2.61689e25	+	2.61689e25i	−0.110410	+	0.110410i
$326$		0			0
$327$			4.75209e26i			1.87989i
$328$		0			0
$329$		−	1.47673e26i		−	0.547954i
$330$		0			0
$331$	3.09901e26	−	3.09901e26i	1.07902	−	1.07902i	0.0824216	−	0.996598i	$-0.473735\pi$
$331$	3.09901e26	−	3.09901e26i	1.07902	−	1.07902i	0.996598	−	0.0824216i	$-0.0262654\pi$
$332$		0			0
$333$	5.26097e26	+	5.26097e26i	1.71950	+	1.71950i
$334$		0			0
$335$	−2.28262e25			−0.0700590
$336$		0			0
$337$	−5.21303e26			−1.50306			−0.751530	−	0.659699i	$-0.770684\pi$
$337$	−5.21303e26			−1.50306			−0.751530	+	0.659699i	$0.770684\pi$
$338$		0			0
$339$	7.92375e26	+	7.92375e26i	2.14701	+	2.14701i
$340$		0			0
$341$	−4.09000e26	+	4.09000e26i	−1.04184	+	1.04184i
$342$		0			0
$343$		−	8.54971e25i		−	0.204816i
$344$		0			0
$345$			3.25833e26i			0.734336i
$346$		0			0
$347$	3.21524e26	−	3.21524e26i	0.681953	−	0.681953i	−0.278487	−	0.960440i	$-0.589833\pi$
$347$	3.21524e26	−	3.21524e26i	0.681953	−	0.681953i	0.960440	+	0.278487i	$0.0898330\pi$
$348$		0			0
$349$	4.77175e26	+	4.77175e26i	0.952820	+	0.952820i	0.998936	−	0.0461156i	$-0.0146843\pi$
$349$	4.77175e26	+	4.77175e26i	0.952820	+	0.952820i	−0.0461156	+	0.998936i	$0.514684\pi$
$350$		0			0
$351$	−1.98696e26			−0.373650
$352$		0			0
$353$	3.64220e26			0.645252			0.322626	−	0.946527i	$-0.395434\pi$
$353$	3.64220e26			0.645252			0.322626	+	0.946527i	$0.395434\pi$
$354$		0			0
$355$	4.45859e25	+	4.45859e25i	0.0744389	+	0.0744389i
$356$		0			0
$357$	1.72007e27	−	1.72007e27i	2.70726	−	2.70726i
$358$		0			0
$359$		−	6.77780e26i		−	1.00600i	−0.864287	−	0.502999i	$-0.832230\pi$
$359$		−	6.77780e26i		−	1.00600i	0.864287	−	0.502999i	$-0.167770\pi$
$360$		0			0
$361$			1.04824e27i			1.46770i
$362$		0			0
$363$	1.14497e27	−	1.14497e27i	1.51278	−	1.51278i
$364$		0			0
$365$	1.48863e26	+	1.48863e26i	0.185657	+	0.185657i
$366$		0			0
$367$	−9.92356e26			−1.16862			−0.584311	−	0.811530i	$-0.698635\pi$
$367$	−9.92356e26			−1.16862			−0.584311	+	0.811530i	$0.698635\pi$
$368$		0			0
$369$	1.09794e27			1.22125
$370$		0			0
$371$	1.34172e27	+	1.34172e27i	1.41005	+	1.41005i
$372$		0			0
$373$	−2.21469e26	+	2.21469e26i	−0.219974	+	0.219974i	−0.808487	−	0.588514i	$-0.799713\pi$
$373$	−2.21469e26	+	2.21469e26i	−0.219974	+	0.219974i	0.588514	+	0.808487i	$0.299713\pi$
$374$		0			0
$375$			1.43717e27i			1.34952i
$376$		0			0
$377$		−	1.21303e26i		−	0.107718i
$378$		0			0
$379$	−7.14103e25	+	7.14103e25i	−0.0599859	+	0.0599859i	−0.736463	−	0.676477i	$-0.763506\pi$
$379$	−7.14103e25	+	7.14103e25i	−0.0599859	+	0.0599859i	0.676477	+	0.736463i	$0.263506\pi$
$380$		0			0
$381$	1.71926e25	+	1.71926e25i	0.0136656	+	0.0136656i
$382$		0			0
$383$	1.63715e27			1.23169			0.615843	−	0.787869i	$-0.288816\pi$
$383$	1.63715e27			1.23169			0.615843	+	0.787869i	$0.288816\pi$
$384$		0			0
$385$	−1.27950e27			−0.911389
$386$		0			0
$387$	1.28570e27	+	1.28570e27i	0.867309	+	0.867309i
$388$		0			0
$389$	−1.17091e27	+	1.17091e27i	−0.748259	+	0.748259i	−0.974152	−	0.225893i	$-0.927470\pi$
$389$	−1.17091e27	+	1.17091e27i	−0.748259	+	0.748259i	0.225893	+	0.974152i	$0.427470\pi$
$390$		0			0
$391$		−	2.43026e27i		−	1.47162i
$392$		0			0
$393$		−	3.48595e27i		−	2.00078i
$394$		0			0
$395$	−3.62536e25	+	3.62536e25i	−0.0197279	+	0.0197279i
$396$		0			0
$397$	4.05449e25	+	4.05449e25i	0.0209236	+	0.0209236i	0.717491	−	0.696568i	$-0.245290\pi$
$397$	4.05449e25	+	4.05449e25i	0.0209236	+	0.0209236i	−0.696568	+	0.717491i	$0.745290\pi$
$398$		0			0
$399$	−8.28838e27			−4.05746
$400$		0			0
$401$	−9.71024e26			−0.451039			−0.225520	−	0.974239i	$-0.572408\pi$
$401$	−9.71024e26			−0.451039			−0.225520	+	0.974239i	$0.572408\pi$
$402$		0			0
$403$	3.00938e26	+	3.00938e26i	0.132670	+	0.132670i
$404$		0			0
$405$	−9.66950e26	+	9.66950e26i	−0.404693	+	0.404693i
$406$		0			0
$407$			4.29738e27i			1.70790i
$408$		0			0
$409$			8.88599e25i			0.0335437i	0.999859	+	0.0167719i	$0.00533890\pi$
$409$			8.88599e25i			0.0335437i	−0.999859	+	0.0167719i	$0.994661\pi$
$410$		0			0
$411$	−1.22166e27	+	1.22166e27i	−0.438139	+	0.438139i
$412$		0			0
$413$	3.15589e27	+	3.15589e27i	1.07559	+	1.07559i
$414$		0			0
$415$	7.29147e25			0.0236216
$416$		0			0
$417$	−7.49809e27			−2.30952
$418$		0			0
$419$	−2.67901e27	−	2.67901e27i	−0.784743	−	0.784743i	0.195884	−	0.980627i	$-0.437242\pi$
$419$	−2.67901e27	−	2.67901e27i	−0.784743	−	0.784743i	−0.980627	+	0.195884i	$0.937242\pi$
$420$		0			0
$421$	3.47449e27	−	3.47449e27i	0.968120	−	0.968120i	−0.0313874	−	0.999507i	$-0.509993\pi$
$421$	3.47449e27	−	3.47449e27i	0.968120	−	0.968120i	0.999507	+	0.0313874i	$0.00999257\pi$
$422$		0			0
$423$		−	2.99175e27i		−	0.793144i
$424$		0			0
$425$		−	4.84410e27i		−	1.22216i
$426$		0			0
$427$	2.75158e27	−	2.75158e27i	0.660830	−	0.660830i
$428$		0			0
$429$	−1.53773e27	−	1.53773e27i	−0.351625	−	0.351625i
$430$		0			0
$431$	1.33425e27			0.290553			0.145276	−	0.989391i	$-0.453593\pi$
$431$	1.33425e27			0.290553			0.145276	+	0.989391i	$0.453593\pi$
$432$		0			0
$433$	1.98332e27			0.411405			0.205703	−	0.978615i	$-0.434052\pi$
$433$	1.98332e27			0.411405			0.205703	+	0.978615i	$0.434052\pi$
$434$		0			0
$435$	−1.50526e27	−	1.50526e27i	−0.297492	−	0.297492i
$436$		0			0
$437$	−5.85525e27	+	5.85525e27i	−1.10278	+	1.10278i
$438$		0			0
$439$			8.80300e27i			1.58035i	0.612881	+	0.790175i	$0.290011\pi$
$439$			8.80300e27i			1.58035i	−0.612881	+	0.790175i	$0.709989\pi$
$440$		0			0
$441$		−	1.41036e28i		−	2.41392i
$442$		0			0
$443$	2.58131e27	−	2.58131e27i	0.421309	−	0.421309i	−0.464345	−	0.885654i	$-0.653710\pi$
$443$	2.58131e27	−	2.58131e27i	0.421309	−	0.421309i	0.885654	+	0.464345i	$0.153710\pi$
$444$		0			0
$445$	−9.84627e26	−	9.84627e26i	−0.153282	−	0.153282i
$446$		0			0
$447$	−1.31022e28			−1.94588
$448$		0			0
$449$	1.66494e27			0.235946			0.117973	−	0.993017i	$-0.462360\pi$
$449$	1.66494e27			0.235946			0.117973	+	0.993017i	$0.462360\pi$
$450$		0			0
$451$	4.48424e27	+	4.48424e27i	0.606506	+	0.606506i
$452$		0			0
$453$	−1.52815e28	+	1.52815e28i	−1.97303	+	1.97303i
$454$		0			0
$455$			9.41444e26i			0.116058i
$456$		0			0
$457$		−	1.04266e28i		−	1.22750i	−0.789501	−	0.613750i	$-0.789660\pi$
$457$		−	1.04266e28i		−	1.22750i	0.789501	−	0.613750i	$-0.210340\pi$
$458$		0			0
$459$	1.83902e28	−	1.83902e28i	2.06802	−	2.06802i
$460$		0			0
$461$	−2.03523e27	−	2.03523e27i	−0.218652	−	0.218652i	0.589278	−	0.807930i	$-0.299412\pi$
$461$	−2.03523e27	−	2.03523e27i	−0.218652	−	0.218652i	−0.807930	+	0.589278i	$0.799412\pi$
$462$		0			0
$463$	−5.92350e27			−0.608104			−0.304052	−	0.952655i	$-0.598340\pi$
$463$	−5.92350e27			−0.608104			−0.304052	+	0.952655i	$0.598340\pi$
$464$		0			0
$465$	7.46872e27			0.732808
$466$		0			0
$467$	−3.67120e27	−	3.67120e27i	−0.344335	−	0.344335i	0.513660	−	0.857994i	$-0.328289\pi$
$467$	−3.67120e27	−	3.67120e27i	−0.344335	−	0.344335i	−0.857994	+	0.513660i	$0.828289\pi$
$468$		0			0
$469$	1.92902e27	−	1.92902e27i	0.172991	−	0.172991i
$470$		0			0
$471$		−	1.41541e28i		−	1.21385i
$472$		0			0
$473$			1.05021e28i			0.861460i
$474$		0			0
$475$	−1.16709e28	+	1.16709e28i	−0.915848	+	0.915848i
$476$		0			0
$477$	2.71823e28	+	2.71823e28i	2.04100	+	2.04100i
$478$		0			0
$479$	2.00681e28			1.44206			0.721030	−	0.692903i	$-0.243669\pi$
$479$	2.00681e28			1.44206			0.721030	+	0.692903i	$0.243669\pi$
$480$		0			0
$481$	3.16197e27			0.217487
$482$		0			0
$483$	−2.75358e28	−	2.75358e28i	−1.81323	−	1.81323i
$484$		0			0
$485$	−1.91808e27	+	1.91808e27i	−0.120942	+	0.120942i
$486$		0			0
$487$		−	2.46609e28i		−	1.48921i	−0.667508	−	0.744603i	$-0.732639\pi$
$487$		−	2.46609e28i		−	1.48921i	0.667508	−	0.744603i	$-0.267361\pi$
$488$		0			0
$489$		−	4.88229e28i		−	2.82410i
$490$		0			0
$491$	−4.19718e26	+	4.19718e26i	−0.0232596	+	0.0232596i	−0.718641	−	0.695381i	$-0.755235\pi$
$491$	−4.19718e26	+	4.19718e26i	−0.0232596	+	0.0232596i	0.695381	+	0.718641i	$0.255235\pi$
$492$		0			0
$493$	1.12272e28	+	1.12272e28i	0.596180	+	0.596180i
$494$		0			0
$495$	−2.59218e28			−1.31920
$496$		0			0
$497$	−7.53582e27			−0.367611
$498$		0			0
$499$	1.34722e28	+	1.34722e28i	0.630062	+	0.630062i	0.948083	−	0.318022i	$-0.103019\pi$
$499$	1.34722e28	+	1.34722e28i	0.630062	+	0.630062i	−0.318022	+	0.948083i	$0.603019\pi$
$500$		0			0
$501$	−1.30809e28	+	1.30809e28i	−0.586601	+	0.586601i
$502$		0			0
$503$			1.89582e28i			0.815329i	0.913132	+	0.407665i	$0.133657\pi$
$503$			1.89582e28i			0.815329i	−0.913132	+	0.407665i	$0.866343\pi$
$504$		0			0
$505$			4.27178e27i			0.176218i
$506$		0			0
$507$	3.04163e28	−	3.04163e28i	1.20371	−	1.20371i
$508$		0			0
$509$	7.98866e27	+	7.98866e27i	0.303345	+	0.303345i	0.842321	−	0.538976i	$-0.181189\pi$
$509$	7.98866e27	+	7.98866e27i	0.303345	+	0.303345i	−0.538976	+	0.842321i	$0.681189\pi$
$510$		0			0
$511$	−2.51605e28			−0.916852
$512$		0			0
$513$	−8.86157e28			−3.09940
$514$		0			0
$515$	9.99858e27	+	9.99858e27i	0.335709	+	0.335709i
$516$		0			0
$517$	1.22190e28	−	1.22190e28i	0.393897	−	0.393897i
$518$		0			0
$519$			9.45605e28i			2.92720i
$520$		0			0
$521$			4.40513e28i			1.30967i	0.755771	+	0.654836i	$0.227262\pi$
$521$			4.40513e28i			1.30967i	−0.755771	+	0.654836i	$0.772738\pi$
$522$		0			0
$523$	−3.82450e28	+	3.82450e28i	−1.09221	+	1.09221i	−0.0969183	+	0.995292i	$0.530899\pi$
$523$	−3.82450e28	+	3.82450e28i	−1.09221	+	1.09221i	−0.995292	+	0.0969183i	$0.969101\pi$
$524$		0			0
$525$	−5.48856e28	−	5.48856e28i	−1.50586	−	1.50586i
$526$		0			0
$527$	−5.57062e28			−1.46856
$528$		0			0
$529$	5.66681e26			0.0143567
$530$		0			0
$531$	6.39362e28	+	6.39362e28i	1.55688	+	1.55688i
$532$		0			0
$533$	3.29945e27	−	3.29945e27i	0.0772336	−	0.0772336i
$534$		0			0
$535$		−	1.67686e28i		−	0.377382i
$536$		0			0
$537$		−	2.17918e28i		−	0.471589i
$538$		0			0
$539$	5.76019e28	−	5.76019e28i	1.19882	−	1.19882i
$540$		0			0
$541$	1.61872e28	+	1.61872e28i	0.324041	+	0.324041i	0.850315	−	0.526274i	$-0.176411\pi$
$541$	1.61872e28	+	1.61872e28i	0.324041	+	0.324041i	−0.526274	+	0.850315i	$0.676411\pi$
$542$		0			0
$543$	−2.66459e28			−0.513136
$544$		0			0
$545$	2.40730e28			0.446033
$546$		0			0
$547$	7.44953e28	+	7.44953e28i	1.32820	+	1.32820i	0.906943	+	0.421253i	$0.138410\pi$
$547$	7.44953e28	+	7.44953e28i	1.32820	+	1.32820i	0.421253	+	0.906943i	$0.361590\pi$
$548$		0			0
$549$	5.57451e28	−	5.57451e28i	0.956526	−	0.956526i
$550$		0			0
$551$		−	5.40995e28i		−	0.893515i
$552$		0			0
$553$		−	6.12750e27i		−	0.0974248i
$554$		0			0
$555$	3.92371e28	−	3.92371e28i	0.600649	−	0.600649i
$556$		0			0
$557$	−8.80710e27	−	8.80710e27i	−0.129824	−	0.129824i	0.639209	−	0.769033i	$-0.279262\pi$
$557$	−8.80710e27	−	8.80710e27i	−0.129824	−	0.129824i	−0.769033	+	0.639209i	$0.779262\pi$
$558$		0			0
$559$	7.72735e27			0.109700
$560$		0			0
$561$	2.84648e29			3.89223
$562$		0			0
$563$	4.72577e28	+	4.72577e28i	0.622494	+	0.622494i	0.946168	−	0.323675i	$-0.104918\pi$
$563$	4.72577e28	+	4.72577e28i	0.622494	+	0.622494i	−0.323675	+	0.946168i	$0.604918\pi$
$564$		0			0
$565$	4.01399e28	−	4.01399e28i	0.509411	−	0.509411i
$566$		0			0
$567$		−	1.63432e29i		−	1.99855i
$568$		0			0
$569$			7.22370e28i			0.851297i	0.904889	+	0.425649i	$0.139954\pi$
$569$			7.22370e28i			0.851297i	−0.904889	+	0.425649i	$0.860046\pi$
$570$		0			0
$571$	−3.90692e28	+	3.90692e28i	−0.443768	+	0.443768i	−0.893276	−	0.449508i	$-0.851599\pi$
$571$	−3.90692e28	+	3.90692e28i	−0.443768	+	0.443768i	0.449508	+	0.893276i	$0.351599\pi$
$572$		0			0
$573$	1.42703e29	+	1.42703e29i	1.56246	+	1.56246i
$574$		0			0
$575$	−7.75469e28			−0.818563
$576$		0			0
$577$	−1.66093e29			−1.69046			−0.845231	−	0.534402i	$-0.820537\pi$
$577$	−1.66093e29			−1.69046			−0.845231	+	0.534402i	$0.820537\pi$
$578$		0			0
$579$	1.25308e28	+	1.25308e28i	0.122985	+	0.122985i
$580$		0			0
$581$	−6.16195e27	+	6.16195e27i	−0.0583268	+	0.0583268i
$582$		0			0
$583$			2.22037e29i			2.02724i
$584$		0			0
$585$			1.90730e28i			0.167990i
$586$		0			0
$587$	−1.61341e28	+	1.61341e28i	−0.137103	+	0.137103i	−0.772327	−	0.635225i	$-0.780907\pi$
$587$	−1.61341e28	+	1.61341e28i	−0.137103	+	0.137103i	0.635225	+	0.772327i	$0.280907\pi$
$588$		0			0
$589$	1.34214e29	+	1.34214e29i	1.10049	+	1.10049i
$590$		0			0
$591$	4.37138e29			3.45899
$592$		0			0
$593$	−1.24782e29			−0.952965			−0.476483	−	0.879184i	$-0.658088\pi$
$593$	−1.24782e29			−0.952965			−0.476483	+	0.879184i	$0.658088\pi$
$594$		0			0
$595$	−8.71348e28	−	8.71348e28i	−0.642338	−	0.642338i
$596$		0			0
$597$	−1.18448e29	+	1.18448e29i	−0.842943	+	0.842943i
$598$		0			0
$599$			1.88628e29i			1.29606i	0.761615	+	0.648030i	$0.224407\pi$
$599$			1.88628e29i			1.29606i	−0.761615	+	0.648030i	$0.775593\pi$
$600$		0			0
$601$			1.02716e29i			0.681484i	0.940157	+	0.340742i	$0.110678\pi$
$601$			1.02716e29i			0.681484i	−0.940157	+	0.340742i	$0.889322\pi$
$602$		0			0
$603$	3.90806e28	−	3.90806e28i	0.250397	−	0.250397i
$604$		0			0
$605$	−5.80016e28	−	5.80016e28i	−0.358929	−	0.358929i
$606$		0			0
$607$	9.20192e28			0.550043			0.275022	−	0.961438i	$-0.411315\pi$
$607$	9.20192e28			0.550043			0.275022	+	0.961438i	$0.411315\pi$
$608$		0			0
$609$	2.54417e29			1.46914
$610$		0			0
$611$	−8.99057e27	−	8.99057e27i	−0.0501597	−	0.0501597i
$612$		0			0
$613$	1.02511e29	−	1.02511e29i	0.552632	−	0.552632i	−0.374568	−	0.927199i	$-0.622209\pi$
$613$	1.02511e29	−	1.02511e29i	0.552632	−	0.552632i	0.927199	+	0.374568i	$0.122209\pi$
$614$		0			0
$615$		−	8.18864e28i		−	0.426602i
$616$		0			0
$617$		−	2.53932e29i		−	1.27857i	−0.768972	−	0.639283i	$-0.779231\pi$
$617$		−	2.53932e29i		−	1.27857i	0.768972	−	0.639283i	$-0.220769\pi$
$618$		0			0
$619$	−1.04494e29	+	1.04494e29i	−0.508558	+	0.508558i	−0.914084	−	0.405526i	$-0.867089\pi$
$619$	−1.04494e29	+	1.04494e29i	−0.508558	+	0.508558i	0.405526	+	0.914084i	$0.367089\pi$
$620$		0			0
$621$	−2.94401e29	−	2.94401e29i	−1.38509	−	1.38509i
$622$		0			0
$623$	1.66420e29			0.756972
$624$		0			0
$625$	−1.14667e29			−0.504309
$626$		0			0
$627$	−6.85807e29	−	6.85807e29i	−2.91671	−	2.91671i
$628$		0			0
$629$	−2.92654e29	+	2.92654e29i	−1.20371	+	1.20371i
$630$		0			0
$631$		−	3.00172e29i		−	1.19416i	−0.802182	−	0.597080i	$-0.796328\pi$
$631$		−	3.00172e29i		−	1.19416i	0.802182	−	0.597080i	$-0.203672\pi$
$632$		0			0
$633$			1.11483e28i			0.0429012i
$634$		0			0
$635$	8.70939e26	−	8.70939e26i	0.00324238	−	0.00324238i
$636$		0			0
$637$	−4.23828e28	−	4.23828e28i	−0.152660	−	0.152660i
$638$		0			0
$639$	−1.52670e29			−0.532103
$640$		0			0
$641$	2.89613e29			0.976808			0.488404	−	0.872618i	$-0.337579\pi$
$641$	2.89613e29			0.976808			0.488404	+	0.872618i	$0.337579\pi$
$642$		0			0
$643$	2.77322e29	+	2.77322e29i	0.905253	+	0.905253i	0.995884	−	0.0906317i	$-0.0288886\pi$
$643$	2.77322e29	+	2.77322e29i	0.905253	+	0.905253i	−0.0906317	+	0.995884i	$0.528889\pi$
$644$		0			0
$645$	9.58894e28	−	9.58894e28i	0.302966	−	0.302966i
$646$		0			0
$647$			1.13910e29i			0.348391i	0.984711	+	0.174195i	$0.0557324\pi$
$647$			1.13910e29i			0.348391i	−0.984711	+	0.174195i	$0.944268\pi$
$648$		0			0
$649$			5.22258e29i			1.54638i
$650$		0			0
$651$	−6.31174e29	+	6.31174e29i	−1.80946	+	1.80946i
$652$		0			0
$653$	1.45323e29	+	1.45323e29i	0.403409	+	0.403409i	0.879433	−	0.476023i	$-0.157922\pi$
$653$	1.45323e29	+	1.45323e29i	0.403409	+	0.403409i	−0.476023	+	0.879433i	$0.657922\pi$
$654$		0			0
$655$	−1.76590e29			−0.474715
$656$		0			0
$657$	−5.09733e29			−1.32711
$658$		0			0
$659$	−4.24768e28	−	4.24768e28i	−0.107116	−	0.107116i	0.651518	−	0.758634i	$-0.274133\pi$
$659$	−4.24768e28	−	4.24768e28i	−0.107116	−	0.107116i	−0.758634	+	0.651518i	$0.774133\pi$
$660$		0			0
$661$	−4.37328e29	+	4.37328e29i	−1.06830	+	1.06830i	−0.0708080	+	0.997490i	$0.522558\pi$
$661$	−4.37328e29	+	4.37328e29i	−1.06830	+	1.06830i	−0.997490	+	0.0708080i	$0.977442\pi$
$662$		0			0
$663$		−	2.09441e29i		−	0.495644i
$664$		0			0
$665$			4.19870e29i			0.962693i
$666$		0			0
$667$	1.79731e29	−	1.79731e29i	0.399301	−	0.399301i
$668$		0			0
$669$	−1.02932e30	−	1.02932e30i	−2.21603	−	2.21603i
$670$		0			0
$671$	4.55349e29			0.950076
$672$		0			0
$673$	4.15844e29			0.840954			0.420477	−	0.907303i	$-0.361863\pi$
$673$	4.15844e29			0.840954			0.420477	+	0.907303i	$0.361863\pi$
$674$		0			0
$675$	−5.86813e29	−	5.86813e29i	−1.15030	−	1.15030i
$676$		0			0
$677$	−3.66467e27	+	3.66467e27i	−0.00696393	+	0.00696393i	−0.710580	−	0.703616i	$-0.751567\pi$
$677$	−3.66467e27	+	3.66467e27i	−0.00696393	+	0.00696393i	0.703616	+	0.710580i	$0.251567\pi$
$678$		0			0
$679$		−	3.24189e29i		−	0.597264i
$680$		0			0
$681$		−	1.15418e30i		−	2.06172i
$682$		0			0
$683$	−2.67612e29	+	2.67612e29i	−0.463541	+	0.463541i	−0.899814	−	0.436273i	$-0.856298\pi$
$683$	−2.67612e29	+	2.67612e29i	−0.463541	+	0.463541i	0.436273	+	0.899814i	$0.356298\pi$
$684$		0			0
$685$	6.18866e28	+	6.18866e28i	0.103955	+	0.103955i
$686$		0			0
$687$	−3.38947e29			−0.552187
$688$		0			0
$689$	1.63372e29			0.258152
$690$		0			0
$691$	5.31525e29	+	5.31525e29i	0.814712	+	0.814712i	0.985336	−	0.170624i	$-0.0545785\pi$
$691$	5.31525e29	+	5.31525e29i	0.814712	+	0.814712i	−0.170624	+	0.985336i	$0.554578\pi$
$692$		0			0
$693$	2.19063e30	−	2.19063e30i	3.25739	−	3.25739i
$694$		0			0
$695$			3.79836e29i			0.547969i
$696$		0			0
$697$			6.10758e29i			0.854919i
$698$		0			0
$699$	1.36974e29	−	1.36974e29i	0.186049	−	0.186049i
$700$		0			0
$701$	3.87829e29	+	3.87829e29i	0.511211	+	0.511211i	0.914898	−	0.403686i	$-0.132271\pi$
$701$	3.87829e29	+	3.87829e29i	0.511211	+	0.511211i	−0.403686	+	0.914898i	$0.632271\pi$
$702$		0			0
$703$	1.41019e30			1.80404
$704$		0			0
$705$	−2.23130e29			−0.277059
$706$		0			0
$707$	−3.61004e29	−	3.61004e29i	−0.435119	−	0.435119i
$708$		0			0
$709$	−1.68164e29	+	1.68164e29i	−0.196765	+	0.196765i	−0.798612	−	0.601847i	$-0.794432\pi$
$709$	−1.68164e29	+	1.68164e29i	−0.196765	+	0.196765i	0.601847	+	0.798612i	$0.294432\pi$
$710$		0			0
$711$		−	1.24139e29i		−	0.141019i
$712$		0			0
$713$			8.91775e29i			0.983593i
$714$		0			0
$715$	−7.78982e28	+	7.78982e28i	−0.0834284	+	0.0834284i
$716$		0			0
$717$	−1.84591e30	−	1.84591e30i	−1.91982	−	1.91982i
$718$		0			0
$719$	−6.34019e28			−0.0640396			−0.0320198	−	0.999487i	$-0.510194\pi$
$719$	−6.34019e28			−0.0640396			−0.0320198	+	0.999487i	$0.510194\pi$
$720$		0			0
$721$	−1.68994e30			−1.65787
$722$		0			0
$723$	5.55352e29	+	5.55352e29i	0.529195	+	0.529195i
$724$		0			0
$725$	3.58247e29	−	3.58247e29i	0.331614	−	0.331614i
$726$		0			0
$727$		−	1.30125e30i		−	1.17017i	−0.810972	−	0.585086i	$-0.801061\pi$
$727$		−	1.30125e30i		−	1.17017i	0.810972	−	0.585086i	$-0.198939\pi$
$728$		0			0
$729$			6.76221e29i			0.590813i
$730$		0			0
$731$	−7.15200e29	+	7.15200e29i	−0.607149	+	0.607149i
$732$		0			0
$733$	−4.12501e29	−	4.12501e29i	−0.340278	−	0.340278i	0.516194	−	0.856472i	$-0.327348\pi$
$733$	−4.12501e29	−	4.12501e29i	−0.340278	−	0.340278i	−0.856472	+	0.516194i	$0.827348\pi$
$734$		0			0
$735$	−1.05187e30			−0.843224
$736$		0			0
$737$	3.19227e29			0.248709
$738$		0			0
$739$	−6.00578e28	−	6.00578e28i	−0.0454781	−	0.0454781i	0.684002	−	0.729480i	$-0.260238\pi$
$739$	−6.00578e28	−	6.00578e28i	−0.0454781	−	0.0454781i	−0.729480	+	0.684002i	$0.760238\pi$
$740$		0			0
$741$	−5.04609e29	+	5.04609e29i	−0.371419	+	0.371419i
$742$		0			0
$743$			8.94934e29i			0.640337i	0.947361	+	0.320168i	$0.103739\pi$
$743$			8.94934e29i			0.640337i	−0.947361	+	0.320168i	$0.896261\pi$
$744$		0			0
$745$			6.63728e29i			0.461689i
$746$		0			0
$747$	−1.24837e29	+	1.24837e29i	−0.0844259	+	0.0844259i
$748$		0			0
$749$	1.41709e30	+	1.41709e30i	0.931836	+	0.931836i
$750$		0			0
$751$	−1.50887e30			−0.964792			−0.482396	−	0.875953i	$-0.660233\pi$
$751$	−1.50887e30			−0.964792			−0.482396	+	0.875953i	$0.660233\pi$
$752$		0			0
$753$	1.74632e30			1.08587
$754$		0			0
$755$	7.74124e29	+	7.74124e29i	0.468131	+	0.468131i
$756$		0			0
$757$	5.95005e28	−	5.95005e28i	0.0349956	−	0.0349956i	−0.689392	−	0.724388i	$-0.742122\pi$
$757$	5.95005e28	−	5.95005e28i	0.0349956	−	0.0349956i	0.724388	+	0.689392i	$0.242122\pi$
$758$		0			0
$759$		−	4.55681e30i		−	2.60688i
$760$		0			0
$761$		−	6.19594e28i		−	0.0344801i	−0.999851	−	0.0172400i	$-0.994512\pi$
$761$		−	6.19594e28i		−	0.0344801i	0.999851	−	0.0172400i	$-0.00548795\pi$
$762$		0			0
$763$	−2.03439e30	+	2.03439e30i	−1.10135	+	1.10135i
$764$		0			0
$765$	−1.76529e30	−	1.76529e30i	−0.929761	−	0.929761i
$766$		0			0
$767$	3.84271e29			0.196919
$768$		0			0
$769$	−1.48010e30			−0.738015			−0.369008	−	0.929426i	$-0.620302\pi$
$769$	−1.48010e30			−0.738015			−0.369008	+	0.929426i	$0.620302\pi$
$770$		0			0
$771$	−1.82462e30	−	1.82462e30i	−0.885323	−	0.885323i
$772$		0			0
$773$	−1.19025e29	+	1.19025e29i	−0.0562022	+	0.0562022i	−0.734649	−	0.678447i	$-0.762653\pi$
$773$	−1.19025e29	+	1.19025e29i	−0.0562022	+	0.0562022i	0.678447	+	0.734649i	$0.262653\pi$
$774$		0			0
$775$			1.77753e30i			0.816861i
$776$		0			0
$777$			6.63178e30i			2.96626i
$778$		0			0
$779$	1.47151e30	−	1.47151e30i	0.640647	−	0.640647i
$780$		0			0
$781$	−6.23538e29	−	6.23538e29i	−0.264258	−	0.264258i
$782$		0			0
$783$	2.72011e30			1.12225
$784$		0			0
$785$	−7.17017e29			−0.288004
$786$		0			0
$787$	1.50882e30	+	1.50882e30i	0.590070	+	0.590070i	0.937650	−	0.347581i	$-0.112997\pi$
$787$	1.50882e30	+	1.50882e30i	0.590070	+	0.590070i	−0.347581	+	0.937650i	$0.612997\pi$
$788$		0			0
$789$	−6.15812e29	+	6.15812e29i	−0.234498	+	0.234498i
$790$		0			0
$791$			6.78437e30i			2.51569i
$792$		0			0
$793$		−	3.35041e29i		−	0.120984i
$794$		0			0
$795$	2.02730e30	−	2.02730e30i	0.712956	−	0.712956i
$796$		0			0
$797$	2.61894e30	+	2.61894e30i	0.897043	+	0.897043i	0.995174	−	0.0981305i	$-0.0312863\pi$
$797$	2.61894e30	+	2.61894e30i	0.897043	+	0.897043i	−0.0981305	+	0.995174i	$0.531286\pi$
$798$		0			0
$799$	1.66423e30			0.555230
$800$		0			0
$801$	3.37154e30			1.09569
$802$		0			0
$803$	−2.08186e30	−	2.08186e30i	−0.659080	−	0.659080i
$804$		0			0
$805$	−1.39490e30	+	1.39490e30i	−0.430216	+	0.430216i
$806$		0			0
$807$		−	3.68193e30i		−	1.10638i
$808$		0			0
$809$		−	3.79175e30i		−	1.11015i	−0.831802	−	0.555073i	$-0.812690\pi$
$809$		−	3.79175e30i		−	1.11015i	0.831802	−	0.555073i	$-0.187310\pi$
$810$		0			0
$811$	3.58639e30	−	3.58639e30i	1.02315	−	1.02315i	0.0234231	−	0.999726i	$-0.492544\pi$
$811$	3.58639e30	−	3.58639e30i	1.02315	−	1.02315i	0.999726	−	0.0234231i	$-0.00745649\pi$
$812$		0			0
$813$	6.43086e30	+	6.43086e30i	1.78780	+	1.78780i
$814$		0			0
$815$	−2.47326e30			−0.670061
$816$		0			0
$817$	3.44628e30			0.909954
$818$		0			0
$819$	−1.61184e30	−	1.61184e30i	−0.414802	−	0.414802i
$820$		0			0
$821$	2.24165e30	−	2.24165e30i	0.562296	−	0.562296i	−0.367663	−	0.929959i	$-0.619842\pi$
$821$	2.24165e30	−	2.24165e30i	0.562296	−	0.562296i	0.929959	+	0.367663i	$0.119842\pi$
$822$		0			0
$823$			7.04894e30i			1.72356i	0.507285	+	0.861779i	$0.330649\pi$
$823$			7.04894e30i			1.72356i	−0.507285	+	0.861779i	$0.669351\pi$
$824$		0			0
$825$		−	9.08282e30i		−	2.16498i
$826$		0			0
$827$	−3.55530e30	+	3.55530e30i	−0.826169	+	0.826169i	−0.986984	−	0.160815i	$-0.948588\pi$
$827$	−3.55530e30	+	3.55530e30i	−0.826169	+	0.826169i	0.160815	+	0.986984i	$0.448588\pi$
$828$		0			0
$829$	1.93524e30	+	1.93524e30i	0.438442	+	0.438442i	0.891487	−	0.453046i	$-0.149663\pi$
$829$	1.93524e30	+	1.93524e30i	0.438442	+	0.438442i	−0.453046	+	0.891487i	$0.649663\pi$
$830$		0			0
$831$	1.13159e31			2.49965
$832$		0			0
$833$	7.84544e30			1.68984
$834$		0			0
$835$	6.62651e29	+	6.62651e29i	0.139180	+	0.139180i
$836$		0			0
$837$	−6.74823e30	+	6.74823e30i	−1.38221	+	1.38221i
$838$		0			0
$839$		−	5.95259e30i		−	1.18906i	−0.804072	−	0.594532i	$-0.797337\pi$
$839$		−	5.95259e30i		−	1.18906i	0.804072	−	0.594532i	$-0.202663\pi$
$840$		0			0
$841$		−	3.47223e30i		−	0.676472i
$842$		0			0
$843$	−1.14811e29	+	1.14811e29i	−0.0218170	+	0.0218170i
$844$		0			0
$845$	−1.54082e30	−	1.54082e30i	−0.285599	−	0.285599i
$846$		0			0
$847$	9.80331e30			1.77254
$848$		0			0
$849$	−6.31798e30			−1.11442
$850$		0			0
$851$	4.68496e30	+	4.68496e30i	0.806206	+	0.806206i
$852$		0			0
$853$	1.22814e29	−	1.22814e29i	0.0206197	−	0.0206197i	−0.696722	−	0.717341i	$-0.745359\pi$
$853$	1.22814e29	−	1.22814e29i	0.0206197	−	0.0206197i	0.717341	+	0.696722i	$0.245359\pi$
$854$		0			0
$855$			8.50628e30i			1.39346i
$856$		0			0
$857$		−	4.87085e30i		−	0.778585i	−0.921114	−	0.389293i	$-0.872719\pi$
$857$		−	4.87085e30i		−	0.778585i	0.921114	−	0.389293i	$-0.127281\pi$
$858$		0			0
$859$	−2.91890e29	+	2.91890e29i	−0.0455293	+	0.0455293i	−0.729505	−	0.683976i	$-0.760249\pi$
$859$	−2.91890e29	+	2.91890e29i	−0.0455293	+	0.0455293i	0.683976	+	0.729505i	$0.260249\pi$
$860$		0			0
$861$	6.92014e30	+	6.92014e30i	1.05337	+	1.05337i
$862$		0			0
$863$	−8.09863e30			−1.20309			−0.601545	−	0.798839i	$-0.705448\pi$
$863$	−8.09863e30			−1.20309			−0.601545	+	0.798839i	$0.705448\pi$
$864$		0			0
$865$	4.79022e30			0.694523
$866$		0			0
$867$	1.05623e31	+	1.05623e31i	1.49472	+	1.49472i
$868$		0			0
$869$	5.07009e29	−	5.07009e29i	0.0700339	−	0.0700339i
$870$		0			0
$871$		−	2.34884e29i		−	0.0316711i
$872$		0			0
$873$		−	6.56785e30i		−	0.864517i
$874$		0			0
$875$	−6.15257e30	+	6.15257e30i	−0.790627	+	0.790627i
$876$		0			0
$877$	−6.65933e30	−	6.65933e30i	−0.835477	−	0.835477i	0.152782	−	0.988260i	$-0.451177\pi$
$877$	−6.65933e30	−	6.65933e30i	−0.835477	−	0.835477i	−0.988260	+	0.152782i	$0.951177\pi$
$878$		0			0
$879$	−2.78903e31			−3.41641
$880$		0			0
$881$	−1.35113e31			−1.61603			−0.808015	−	0.589162i	$-0.799458\pi$
$881$	−1.35113e31			−1.61603			−0.808015	+	0.589162i	$0.799458\pi$
$882$		0			0
$883$	1.22213e30	+	1.22213e30i	0.142734	+	0.142734i	0.774863	−	0.632129i	$-0.217819\pi$
$883$	1.22213e30	+	1.22213e30i	0.142734	+	0.142734i	−0.632129	+	0.774863i	$0.717819\pi$
$884$		0			0
$885$	4.76846e30	−	4.76846e30i	0.543843	−	0.543843i
$886$		0			0
$887$		−	6.83119e30i		−	0.760849i	−0.924812	−	0.380425i	$-0.875778\pi$
$887$		−	6.83119e30i		−	0.760849i	0.924812	−	0.380425i	$-0.124222\pi$
$888$		0			0
$889$			1.47204e29i			0.0160122i
$890$		0			0
$891$	1.35229e31	−	1.35229e31i	1.43666	−	1.43666i
$892$		0			0
$893$	−4.00966e30	−	4.00966e30i	−0.416071	−	0.416071i
$894$		0			0
$895$	−1.10392e30			−0.111892
$896$		0			0
$897$	−3.35285e30			−0.331966
$898$		0			0
$899$	−4.11977e30	−	4.11977e30i	−0.398471	−	0.398471i
$900$		0			0
$901$	−1.51208e31	+	1.51208e31i	−1.42878	+	1.42878i
$902$		0			0
$903$			1.62070e31i			1.49617i
$904$		0			0
$905$			1.34982e30i			0.121749i
$906$		0			0
$907$	1.46625e31	−	1.46625e31i	1.29221	−	1.29221i	0.358789	−	0.933419i	$-0.383190\pi$
$907$	1.46625e31	−	1.46625e31i	1.29221	−	1.29221i	0.933419	−	0.358789i	$-0.116810\pi$
$908$		0			0
$909$	−7.31369e30	−	7.31369e30i	−0.629819	−	0.629819i
$910$		0			0
$911$	−1.88663e31			−1.58761			−0.793805	−	0.608172i	$-0.791903\pi$
$911$	−1.88663e31			−1.58761			−0.793805	+	0.608172i	$0.791903\pi$
$912$		0			0
$913$	−1.01972e30			−0.0838566
$914$		0			0
$915$	−4.15755e30	−	4.15755e30i	−0.334131	−	0.334131i
$916$		0			0
$917$	1.49235e31	−	1.49235e31i	1.17217	−	1.17217i
$918$		0			0
$919$		−	4.74697e30i		−	0.364422i	−0.983259	−	0.182211i	$-0.941675\pi$
$919$		−	4.74697e30i		−	0.364422i	0.983259	−	0.182211i	$-0.0583253\pi$
$920$		0			0
$921$			2.21979e31i			1.66566i
$922$		0			0
$923$	−4.58793e29	+	4.58793e29i	−0.0336511	+	0.0336511i
$924$		0			0
$925$	9.33827e30	+	9.33827e30i	0.669543	+	0.669543i
$926$		0			0
$927$	−3.42370e31			−2.39971
$928$		0			0
$929$	−2.33380e31			−1.59919			−0.799594	−	0.600542i	$-0.794952\pi$
$929$	−2.33380e31			−1.59919			−0.799594	+	0.600542i	$0.794952\pi$
$930$		0			0
$931$	−1.89021e31	−	1.89021e31i	−1.26631	−	1.26631i
$932$		0			0
$933$	9.66260e30	−	9.66260e30i	0.632903	−	0.632903i
$934$		0			0
$935$		−	1.44196e31i		−	0.923491i
$936$		0			0
$937$			4.96132e30i			0.310693i	0.987860	+	0.155346i	$0.0496494\pi$
$937$			4.96132e30i			0.310693i	−0.987860	+	0.155346i	$0.950351\pi$
$938$		0			0
$939$	−1.05897e31	+	1.05897e31i	−0.648477	+	0.648477i
$940$		0			0
$941$	9.68676e30	+	9.68676e30i	0.580079	+	0.580079i	0.934925	−	0.354846i	$-0.115467\pi$
$941$	9.68676e30	+	9.68676e30i	0.580079	+	0.580079i	−0.354846	+	0.934925i	$0.615467\pi$
$942$		0			0
$943$	9.77735e30			0.572596
$944$		0			0
$945$	−2.11110e31			−1.20913
$946$		0			0
$947$	8.03123e30	+	8.03123e30i	0.449891	+	0.449891i	0.895318	−	0.445427i	$-0.146948\pi$
$947$	8.03123e30	+	8.03123e30i	0.449891	+	0.449891i	−0.445427	+	0.895318i	$0.646948\pi$
$948$		0			0
$949$	−1.53181e30	+	1.53181e30i	−0.0839285	+	0.0839285i
$950$		0			0
$951$		−	2.61731e31i		−	1.40268i
$952$		0			0
$953$			1.16414e31i			0.610279i	0.952308	+	0.305140i	$0.0987031\pi$
$953$			1.16414e31i			0.610279i	−0.952308	+	0.305140i	$0.901297\pi$
$954$		0			0
$955$	7.22899e30	−	7.22899e30i	0.370717	−	0.370717i
$956$		0			0
$957$	2.10513e31	+	2.10513e31i	1.05609	+	1.05609i
$958$		0			0
$959$	−1.04599e31			−0.513374
$960$		0			0
$961$	−3.84300e29			−0.0184533
$962$		0			0
$963$	2.87093e31	+	2.87093e31i	1.34880	+	1.34880i
$964$		0			0
$965$	6.34780e29	−	6.34780e29i	0.0291801	−	0.0291801i
$966$		0			0
$967$		−	5.95496e30i		−	0.267856i	−0.990991	−	0.133928i	$-0.957241\pi$
$967$		−	5.95496e30i		−	0.267856i	0.990991	−	0.133928i	$-0.0427590\pi$
$968$		0			0
$969$		−	9.34077e31i		−	4.11133i
$970$		0			0
$971$	1.64188e31	−	1.64188e31i	0.707194	−	0.707194i	−0.258751	−	0.965944i	$-0.583311\pi$
$971$	1.64188e31	−	1.64188e31i	0.707194	−	0.707194i	0.965944	+	0.258751i	$0.0833108\pi$
$972$		0			0
$973$	−3.20996e31	−	3.20996e31i	−1.35305	−	1.35305i
$974$		0			0
$975$	−6.68304e30			−0.275693
$976$		0			0
$977$	5.02907e30			0.203046			0.101523	−	0.994833i	$-0.467628\pi$
$977$	5.02907e30			0.203046			0.101523	+	0.994833i	$0.467628\pi$
$978$		0			0
$979$	1.37701e31	+	1.37701e31i	0.544150	+	0.544150i
$980$		0			0
$981$	−4.12152e31	+	4.12152e31i	−1.59416	+	1.59416i
$982$		0			0
$983$		−	3.40557e31i		−	1.28937i	−0.764448	−	0.644685i	$-0.776989\pi$
$983$		−	3.40557e31i		−	1.28937i	0.764448	−	0.644685i	$-0.223011\pi$
$984$		0			0
$985$		−	2.21444e31i		−	0.820698i
$986$		0			0
$987$	1.88565e31	−	1.88565e31i	0.684116	−	0.684116i
$988$		0			0
$989$	1.14493e31	+	1.14493e31i	0.406648	+	0.406648i
$990$		0			0
$991$	4.84855e31			1.68592			0.842962	−	0.537972i	$-0.180810\pi$
$991$	4.84855e31			1.68592			0.842962	+	0.537972i	$0.180810\pi$
$992$		0			0
$993$	7.91429e31			2.69429
$994$		0			0
$995$	6.00032e30	+	6.00032e30i	0.200001	+	0.200001i
$996$		0			0
$997$	−4.16405e30	+	4.16405e30i	−0.135899	+	0.135899i	−0.771784	−	0.635885i	$-0.780635\pi$
$997$	−4.16405e30	+	4.16405e30i	−0.135899	+	0.135899i	0.635885	+	0.771784i	$0.280635\pi$
$998$		0			0
$999$			7.09040e31i			2.26586i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.22.e.a.17.39		82
4.3	odd	2		16.22.e.a.13.10	yes	82
16.5	even	4	inner	64.22.e.a.49.39		82
16.11	odd	4		16.22.e.a.5.10	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.22.e.a.5.10	✓	82	16.11	odd	4
16.22.e.a.13.10	yes	82	4.3	odd	2
64.22.e.a.17.39		82	1.1	even	1	trivial
64.22.e.a.49.39		82	16.5	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	64.e (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(127691. + 127691. i) q^{3} +(6.46851e6 - 6.46851e6i) q^{5} +1.09329e9i q^{7} +2.21494e10i q^{9} +(-9.04627e10 + 9.04627e10i) q^{11} +(6.65615e10 + 6.65615e10i) q^{13} +1.65194e12 q^{15} -1.23211e13 q^{17} +(2.96854e13 + 2.96854e13i) q^{19} +(-1.39603e14 + 1.39603e14i) q^{21} +1.97243e14i q^{23} +3.93154e14i q^{25} +(-1.49258e15 + 1.49258e15i) q^{27} +(-9.11213e14 - 9.11213e14i) q^{29} +4.52120e15 q^{31} -2.31025e16 q^{33} +(7.07199e15 + 7.07199e15i) q^{35} +(2.37522e16 - 2.37522e16i) q^{37} +1.69985e16i q^{39} -4.95700e16i q^{41} +(5.80467e16 - 5.80467e16i) q^{43} +(1.43274e17 + 1.43274e17i) q^{45} -1.35072e17 q^{47} -6.36747e17 q^{49} +(-1.57329e18 - 1.57329e18i) q^{51} +(1.22723e18 - 1.22723e18i) q^{53} +1.17032e18i q^{55} +7.58110e18i q^{57} +(2.88659e18 - 2.88659e18i) q^{59} +(-2.51678e18 - 2.51678e18i) q^{61} -2.42158e19 q^{63} +8.61108e17 q^{65} +(-1.76441e18 - 1.76441e18i) q^{67} +(-2.51861e19 + 2.51861e19i) q^{69} +6.89277e18i q^{71} +2.30134e19i q^{73} +(-5.02020e19 + 5.02020e19i) q^{75} +(-9.89024e19 - 9.89024e19i) q^{77} -5.60462e18 q^{79} -1.49486e20 q^{81} +(5.63613e18 + 5.63613e18i) q^{83} +(-7.96993e19 + 7.96993e19i) q^{85} -2.32706e20i q^{87} -1.52218e20i q^{89} +(-7.27713e19 + 7.27713e19i) q^{91} +(5.77314e20 + 5.77314e20i) q^{93} +3.84041e20 q^{95} -2.96525e20 q^{97} +(-2.00369e21 - 2.00369e21i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 2 q^{3} - 2 q^{5} - 67333320738 q^{11} - 2 q^{13} - 4613203124996 q^{15} - 4 q^{17} + 46007763621434 q^{19} + 20920706404 q^{21} - 11\!\cdots\!20 q^{27} - 24\!\cdots\!02 q^{29} + 98\!\cdots\!16 q^{31}+ \cdots - 27\!\cdots\!38 q^{99}+O(q^{100}) \) 82 * q + 2 * q^3 - 2 * q^5 - 67333320738 * q^11 - 2 * q^13 - 4613203124996 * q^15 - 4 * q^17 + 46007763621434 * q^19 + 20920706404 * q^21 - 1147760716556920 * q^27 - 2433173450216602 * q^29 + 9835539443769616 * q^31 - 4 * q^33 + 19253478556034884 * q^35 - 7245708527119386 * q^37 - 215332019803969386 * q^43 + 953653395699842 * q^45 - 1051982644716600976 * q^47 - 5585458640832840074 * q^49 - 3238772068175213124 * q^51 + 1889987679210147606 * q^53 - 3631979197965016922 * q^59 + 10385362452353654062 * q^61 + 17464422381302680956 * q^63 - 9364161130572538716 * q^65 + 17102217044572669130 * q^67 - 3951842785111207532 * q^69 - 145960939174166395366 * q^75 - 82041801652678580764 * q^77 - 204448210818924484480 * q^79 - 802405920297757300870 * q^81 - 317463236552669319678 * q^83 + 323656241286464843748 * q^85 - 144326756239046079748 * q^91 - 669717759565183008560 * q^93 + 1411330138695550130700 * q^95 - 4 * q^97 - 2710306841526615010238 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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